BCS-BEC crossover in atomic Fermi gases in quasi-two-dimensional Lieb lattices: Effect of flat band at finite temperature

The superfluid behavior of ultracold atomic Fermi gases with a short range attractive interaction in quasi-two-dimensional Lieb lattices is studied using a pairing fluctuation theory, within the context of BCS-BEC crossover, with a focus on the interplay of finite temperature and flat band. As the Fermi level enters the flat band, the evolution of $T_c$ as a function of interaction strength $g$ changes from the conventional exponential behavior to power law, along with strongly enhanced quantum geometric effects. The temperature dependence of both the superfluid order parameter and the high superfluid density also undergoes a similar change due to the influence of flat band. At relatively high densities and moderate or strong pairing interaction, a pair density wave emerges. In addition, hole-like pairing occurs when the Fermi level crosses the van Hove singularity, leading to nonmonotonic dependence of the chemical potential $mu(g)$ on $g$..